--- title: "Amplitude limiter; FM demodulation using PLL" subject: "Communication Systems" chapter: 3 key: "semester_6/communication_systems:limiter-discriminator-pll-fm" source: https://www.bctengineer.com/q/semester_6/communication_systems/limiter-discriminator-pll-fm site: BCT Engineering --- # Amplitude limiter; FM demodulation using PLL Communication Systems · Chapter 3: Angle Modulation - Asked in: 2076 Bhadra (CS I), 2+4 marks; 2070 Magh (CS I), 2+6 marks (asked 2 times) - Video: [FM Demodulation by Phase Lock Loop (Basics, Block Diagram, Working & Advantages) Explained](https://www.youtube.com/watch?v=30DaodObd9Q) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/limiter-discriminator-pll-fm - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3 ## Question What is the role of amplitude limiter in limiter discriminator method? Explain FM demodulator using PLL. ## Short answer The amplitude limiter strips all amplitude variations from the FM signal before the discriminator so only frequency variations remain, preventing noise and distortion. In a PLL demodulator, a phase detector compares the input FM and VCO output; after loop filtering, the error voltage drives the VCO to track the input phase, making the VCO control voltage proportional to the original message. ## Answer #### Role of the amplitude limiter In a limiter–discriminator FM detector, the **amplitude limiter** removes all amplitude variations of the received FM signal before it reaches the discriminator. - Noise, interference and fading change the amplitude of the FM wave, but the information is only in its frequency. - A discriminator's output depends on both frequency and amplitude, so amplitude changes would appear as noise and distortion. - The limiter (a hard clipper followed by a band-pass filter at the IF) produces a constant-amplitude signal with the same zero crossings, i.e. the same instantaneous frequency. ```text FM + AM noise -> [Hard limiter] -> [BPF] -> constant- /\/\/\ /\/\ square-ish at fc amplitude FM ``` So the discriminator sees only frequency variations, which gives FM its noise immunity. #### FM demodulation using PLL A **phase-locked loop** is a feedback system in which a voltage-controlled oscillator (VCO) is forced to follow the phase, and hence the frequency, of the input. The control voltage needed to do this is the demodulated message. ```text s(t) -->[ Phase ]-->[ Loop ]--+--> v(t) = output [ detector ] [ filter] | (message) ^ | | | +------[ VCO ]<----+ ``` **Blocks** - **Phase detector (multiplier):** compares input and VCO phases and gives an error voltage. - **Loop filter:** low-pass; removes the $2f_c$ term and sets loop dynamics. - **VCO:** its frequency is $f_c + k_vv(t)$. **Analysis** Input FM wave and VCO output: $$ s(t) = A_c\sin[\omega_ct + \phi_1(t)], \quad \phi_1(t) = 2\pi k_f\int_0^t m(\tau)d\tau $$ $$ r(t) = A_v\cos[\omega_ct + \phi_2(t)], \quad \phi_2(t) = 2\pi k_v\int_0^t v(\tau)d\tau $$ The multiplier output, after removing the $2\omega_c$ term, is $$ e(t) = K_m\sin[\phi_1(t) - \phi_2(t)] = K_m\sin\phi_e(t) $$ When the loop is locked, $\phi_e$ is small, so $\sin\phi_e \approx \phi_e$ (linear model). With high loop gain the loop drives $\phi_e \to 0$, so $$ \phi_2(t) \approx \phi_1(t) \;\Rightarrow\; 2\pi k_v\int v(t)dt \approx 2\pi k_f\int m(t)dt $$ Differentiating both sides: $$ v(t) \approx \frac{k_f}{k_v}m(t) $$ The loop filter output is therefore proportional to the message. The PLL demodulator has good threshold performance, needs no tuned circuits, and is available as a single IC (e.g. 565). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is an amplitude limiter placed before the discriminator? A. To boost high audio frequencies B. To reduce the bandwidth C. To restore the carrier D. Because a discriminator output depends on amplitude as well as frequency, so amplitude noise must be removed Answer: D. Information is in the frequency only; the limiter gives constant amplitude with the same zero crossings. (Key point: Why a limiter) 2. In the PLL demodulator, which signal is the demodulated message? A. The VCO output itself B. The control voltage v(t) that steers the VCO C. The multiplier output before the loop filter D. The input carrier Answer: B. The VCO must follow the input frequency, and the control voltage needed to do so is proportional to m(t). (Key point: PLL principle) 3. What is the loop filter's role? A. High-pass to pass 2fc B. Amplitude limiting C. Low-pass to remove the double-frequency term and set loop dynamics D. Frequency doubling Answer: C. It is a low-pass filter removing the 2fc product term and controlling stability. (Key point: Loop filter) 4. In lock with high loop gain, what is v(t)? A. (kv/kf) m(t) B. kf kv m(t) C. (kf/kv) m(t) D. m(t)^2 Answer: C. Setting φ2 ≈ φ1 gives 2πkv∫v = 2πkf∫m, hence v = (kf/kv) m(t). (Key point: Result in lock) ## Related in Communication Systems - [Limiter-discriminator FM demodulation; need for pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator-pre-emphasis) — Communication Systems, chapter 3 - [Limiter-discriminator FM demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator) — Communication Systems, chapter 3 - [FM demodulation using PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-demod-pll) — Communication Systems, chapter 3, asked 2× - [PLL lock and capture range; FM demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apll-lock-capture-fm-demod) — Communication Systems, chapter 3 - [PLL as FM demodulator; uses of PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apll-fm-demod-uses) — Communication Systems, chapter 3 - [Phase error in coherent DSB-SC detection; AM demodulation by PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aphase-error-dsbsc-am-pll) — Communication Systems, chapter 2